📄 gslib help trans.htm
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<HTML><HEAD><TITLE>GSLIB Help: TRANS</TITLE>
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<H2>GSLIB Help Page: TRANS</H2></CENTER>
<DL>
<DT><IMG height=14 alt=o src="GSLIB Help TRANS.files/ball.red.gif" width=14>
<STRONG>Description:</STRONG>
<UL>
<LI><TT>trans</TT> is a generalization of the quantile transformation used
for normal scores, the $p$-quantile of the original distribution is
transformed to the $p$-quantile of the target distribution. This transform
preserves the $p$-quantile indicator variograms of the original values. The
variogram (standardized by the variance) will also be stable provided that
the target distribution is not too different from the initial distribution.
</LI></UL>
<DT><IMG height=14 alt=o src="GSLIB Help TRANS.files/ball.red.gif" width=14>
<STRONG>Parameters:</STRONG>
<UL>
<LI><B>vartype:</B> the variable type (1=continuous, 0=categorical)
<LI><B>refdist:</B> the input data file with the target distribution and
weights.
<LI><B>ivr</B> and <B>iwt:</B> the column for the values and the column for
the (declustering) weight. If there are no declustering weights then set
<B>iwt</B>= 0.
<LI><B>datafl:</B> the input file with the distribution(s) to be
transformed.
<LI><B>ivrd</B> and <B>iwtd:</B> the column for the values and the
declustering weights (0 if none).
<LI><B>tmin</B> and <B>tmax:</B> all values strictly less than <B>tmin</B>
and strictly greater than <B>tmax</B> are ignored.
<LI><B>outfl:</B> output file for the transformed values.
<LI><B>nsets:</B> number of realizations or "sets" to transform. Each set is
transformed separately.
<LI><B>nx, ny,</B> and <B>nz:</B> size of 3-D model (for categorical
variable). When transforming categorical variables it is essential to
consider some type of tie-breaking scheme. A moving window (of the following
size) is considered for tie-breaking when considering a categorical
variable.
<LI><B>wx, wy,</B> and <B>wz:</B> size of 3-D window for categorical
variable tie-breaking.
<LI><B>nxyz:</B> the number to transform at a time (when dealing with a
continuous variable). Recall that <B>nxyz</B> will be considered
<B>nsets</B> times.
<LI><B>zmin</B> and <B>zmax:</B> are the minimum and maximum values that
will be used for extrapolation in the tails.
<LI><B>ltail</B> and <B>ltpar</B> specify the back transformation
implementation in the lower tail of the distribution: $<B>ltail</B>=1$
implements linear interpolation to the lower limit <B>zmin</B> and
$<B>ltail</B>=2$ implements power model interpolation, with <B>w=ltpar</B>,
to the lower limit <B>zmin</B>.
<LI><B>utail</B> and <B>utpar</B> specify the back transformation
implementation in the upper tail of the distribution: $<B>utail</B>=1$
implements linear interpolation to the upper limit <B>zmax</B>
$<B>utail</B>=2$ implements power model interpolation, with <B>w=utpar</B>,
to the upper limit <B>zmax</B>, and $<B>utail</B>=4$ implements hyperbolic
model extrapolation with <B>w=utpar</B>.
<LI><B>transcon:</B> constrain transformation to honor local data? (1=yes,
0=no)
<LI><B>estvfl:</B> an input file with the estimation variance (must be of
size <B>nxyz</B>).
<LI><B>icolev:</B> column number in <B>estvfl</B> for the estimation
variance.
<LI><B>omega:</B> the control parameter for how much weight is given to the
original data (w between 0.33 and 3.0)
<LI><B>seed:</B> random number seed used when constraining a categorical
variable transformation to local data. A short description of the program
</LI></UL>
<DT><IMG height=14 alt=o src="GSLIB Help TRANS.files/ball.red.gif" width=14>
<STRONG>Application notes:</STRONG>
<UL>
<LI>When ``freezing'' the original data values, the quantile transform is
applied progressively as the location gets further away from the set of data
locations. The distance measure used is proportional to a kriging variance
at the location of the value being transformed. That kriging variance is
zero at the data locations (hence no transformation) and increases away from
the data (the transform is increasingly applied). An input kriging variance
file must be provided or, as an option, <TT>trans</TT> can calculate these
kriging variances using an arbitrary isotropic and smooth (Gaussian)
variogram model.
<LI>Because not all original values are transformed, reproduction of the
target histogram is only approximate. A control parameter, w in [0,1],
allows the desired degree of approximation to be achieved at the cost of
generating discontinuities around the data locations. The greater w, the
lesser the discontinuities.
<LI>Program <TT>trans</TT> can be applied to either continuous or
categorical values. In the case of categorical values a hierarchy or spatial
sequencing of the $K$ categories is provided implicitly through the integer
coding $k=1,\ldots,K$ of these categories. Category $k$ may be transformed
into category $(k-1)$ or $(k+1)$ and only rarely into categories further
away.
<LI>An interesting side application of program <TT>trans</TT> is in cleaning
noisy simulated images. Two successive runs (a ``roundtrip'') of
<TT>trans</TT>, the first changing the original proportions or distribution,
the second restituting these original proportions, would clean the original
image while preserving data exactitude. </LI></UL></DT></DL><IMG height=8
alt=--- src="GSLIB Help TRANS.files/line.blue.gif" width=652>
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